Prior art is represented by the Tell-known discrete Fourier transform (DFT) or its case-specific efficient implementation, the fast Fourier transform (FFT). Efficient single and multi-tone frequency measurement can be achieved using the prior art. However, even though such prior art is efficient and has desirable noise-reduction properties, direct frequency measurement accuracy is limited to 2π/N radians.
In response to this deficiency in the prior art, two recently disclosed inventions, the DFT/FFT-based jackknife-localized multi-tone frequency measurement (JKLMTM) apparatus filed on Jun. 12, 2015 as U.S. patent application Ser. No. 14/737,542 and the DFT/FFT-based 1st-order difference multi-tone frequency measurement apparatus (1ODMTM) filed on Jun. 10, 2015 as U.S. patent application Ser. No. 14/735,228, represent methods of precise and accurate single and multi-tone frequency measurement. It remains desirable yet to provide an apparatus that can measure the remaining parameters of tones, specific the amplitude and phase.